Recently, when I was handling a friend's baby, he made a sound that was basically an unvoiced creaky rattle. I tried to comment on it, then realized that I had no idea what word was really used for that rattling sound. I've seen them use it when unhappy or when happy although it's usually used more for mild complaint. As a conscious adult, I make the sound by collapsing the back of the throat and pushing air through. Using it to hit low notes in singing is generally called "creaky voice".
I suspect that it's appealing to the child because it a) makes a distinct sound, b) creates a physical sensation in the back of the throat from the vibrations, and c) is relatively easy to do at an early age, not requiring anything fancy with the mouth or tongue.
If I were pressed to pick a word, I'd probably go for "grumbling" or "grousing". Could those be the actual words used for the sound?
To give an example sentence:
"The baby boy awakened and sleepily blinked his eyes as he ground out a low rattling ___ of complaint, not yet crying, but clearly displeased at this disturbance to his peace and wanting to ensure we knew it."